A Qualitative Model for Reasoning about Path and Support

Summary

This paper presents a hybrid qualitative reasoning model for Camelot Jr., a block puzzle in which a knight must reach a princess via bridges built from a fixed inventory of rectangular blocks and ramp-ended stair blocks under gravity. The authors formalize the game as a grid of cells, define blocks as 4-tuples with an eight-state orientation algebra (horizontal/vertical × mirrored × inverted, with two illegal states pruned), and specify placement constraints covering boundary exclusion, collision, and foundational support — notably that ramp cells cannot carry other blocks, while inverted horizontal stairs provide flat support. Structural integrity is checked with a numerical center-of-mass logic: recursive load aggregation, a convex-hull containment constraint, and a lever rule distributing weight between the outermost supports; the authors argue stability must be validated only after the full inventory is placed, since counterweights can rescue unstable stacks. Path validity is then decided on a directed acyclic graph of move-right, move-diagonal-up and move-diagonal-down actions gated by four cell-affordance conditions, and a recursive backtracking search with geometric pruning explores inventory permutations, orientations and positions. The main limitation is that the paper reports no experiments: no levels solved, success rates, runtimes, ablations or baselines (e.g., general planners or the cited Angry Birds qualitative solver), so the claim that the solver handles arbitrary configuration challenges is unsupported, and no code or level dataset is released.